Quasi-static

Many optical studies have employed a quasi-static cell, through which the photolytic precursor of one of the reagents and the stable molecular reagent are slowly flowed. The reaction is then initiated by laser photolysis of the precursor, and the products are detected a short time after the photolysis event. To avoid collisional relaxation of the internal degrees of freedom of the product, the products must be detected in a shorter time when compared to the time between gas-kinetic collisions, that depends inversely upon the total pressure in the cell. In some cases, for example in case of the stable NO product from the H + NO2 reaction discussed in section B2.3.3.2. the products are not removed by collisions with the walls and may have long residence times in the apparatus. Study of such reactions are better carried out with pulsed introduction of the reagents into the cell or under crossed-beam conditions. 

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

In the limit of very slow change (quasi-static process) the frictional component is zero and then the work done by the external force equals the free energy change, i.e.. 

Let us recall the dependence of solutions to dynamical and quasi-static problems on the time parameter t. Then Hooke s law (1.3) takes the form... 

Here ij denotes a plastic deformation velocity. Adding the relations (1.10), (1.11), we obtain the quasi-static elastoplastic model... 

Here we have assumed that the temperature 9 does not depend on Let the plate be isotropic and aij = Pij = (5 %, where 5 is a constant. Then (1.33) gives the quasi-static model of a thermoelastic plate ... 

Here ij denotes a velocity of a plastic part of the curvature. This model is quasi-static, and it reduces to the equivalent inequality... 

Using physical properties relating to performance parameters leads to the development of algorithms for predicting performance for laboratory screening of potential improvements. Many of these algorithms have been estabUshed. The two main categories of measurement criteria are quasi static and dynamic mechanical properties. 

Shock loading in most metals and alloys produces greater hardening than quasi-static deformation to the same total strain, particularly if the metal undergoes a polymorphic phase transition, such as is observed in pure iron [1]-[10]. Figure 6.1 compares the stress-strain response of an annealed... 

Figure 6.1. Stress-strain behavior of shock-loaded copper compared to the annealed starting condition illustrating an enhanced flow stress following shock-wave deformation compared to quasi-static deformation (based on an equivalent strain basis).

This phenomena has been attributed to the very high strain rates associated with shock loading and the subsonic restriction on dislocation velocity requiring the generation and storage of a larger dislocation density during the shock process than for quasi-static processes [1], [2], [12],... 

To illustrate the effect of radial release interactions on the structure/ property relationships in shock-loaded materials, experiments were conducted on copper shock loaded using several shock-recovery designs that yielded differences in es but all having been subjected to a 10 GPa, 1 fis pulse duration, shock process [13]. Compression specimens were sectioned from these soft recovery samples to measure the reload yield behavior, and examined in the transmission electron microscope (TEM) to study the substructure evolution. The substructure and yield strength of the bulk shock-loaded copper samples were found to depend on the amount of e, in the shock-recovered sample at a constant peak pressure and pulse duration. In Fig. 6.8 the quasi-static reload yield strength of the 10 GPa shock-loaded copper is observed to increase with increasing residual sample strain. 

Figure 6.8. Plot of the quasi-static reloaded yield stress of shock-loaded copper versus the natural logarithm of residual strain for a 10 GPa symmetric shock with 1 /is pulse duration.

In this study, the appearance and evolution sequence of planar slip bands, in addition to a dislocation cell structure with increasing e,, is identical to that observed in quasi-static studies of the effects of stress path changes on dislocation substructure development [27]. The substructure evolution in copper deformed quasi-statically is known to be influenced by changes in stress path [27]. Deforming a sample in tension at 90° orthogonal to the... 

P.S. Follansbee and G.T. Gray III, The Response of Single Crystal and Polycrystal Nickel to Quasi-Static and Shock Deformation, in Advances in Plasticity 1989 (edited by A.S. Khan and M. Tokuda), Pergamon Press, Oxford, 1989, pp. 385-388. 

Figure 7.3. Dislocation densities required to fit the precursor curves as a function of the initial quasi-static yield stress.

Flinn et al. [30] describes an experimental impact technique in which <100)-oriented LiF single crystals ( 8 ppm Mg) are loaded in a controlled manner and the multiplication of screw dislocations is measured. The peak shear stress in this relatively soft material is 0.01 GPa. For shear impulses exceeding approximately 40 dyne s/cm, dislocation multiplication is adequately described by the multiple-cross-glide mechanism [(7.24)] with m = l/bL = (2-4) X 10 m, in reasonable agreement with quasi-static measurement [2]. 

Gray and Follansbee [44] quasi-statically tested OFE copper samples that had been shock loaded to 10 GPa and pulse durations of 0.1 fis, 1 /rs, and 2 fus. The quasi-static stress-strain curves are shown in Fig. 7.10 with the response of annealed starting copper included for comparison. The yield strength of shock-loaded copper is observed to increase with pulse duration, as the work-hardening rate is seen to systematically decrease. 

In this chapter, we overview basic techniques for making nanoscale adhesion and mechanical property measurements. Both quasi-static and dynamic measurements are addressed. In Section 2 of this chapter, we overview basic AFM instrumentation and techniques, while depth-sensing nanoindentation is overviewed in Section 3. Section 4 addresses recent advances in instrumentation and techniques... 

Quasi-static measurements force-distance curves and adhesion... 

Basire and Frctigny [72J to determine the sample modulus quasi-statically for viscous contacts. 

The main results of this miero-mechanical model in the quasi-static regime have been compared with experimental results obtained by placing polystyrene (PS)-polyvinyl pyridine (PVP) diblock copolymers with a short PVP block between PS and PVP homopolymers. The fracture toughness was found to increase linearly with E from that of the bare PS/PVP interface, while the slope of the line increased with the degree of polymerization of the block being pulled out. If the data for the different copolymers were plotted as AG vs. (where... 

A strength value associated with a Hugoniot elastic limit can be compared to quasi-static strengths or dynamic strengths observed values at various loading strain rates by the relation of the longitudinal stress component under the shock compression uniaxial strain tensor to the one-dimensional stress tensor. As shown in Sec. 2.3, the longitudinal components of a stress measured in the uniaxial strain condition of shock compression can be expressed in terms of a combination of an isotropic (hydrostatic) component of pressure and its deviatoric or shear stress component. 

Elsworth et al. (1983) report experiments performed in an open-topped channel 52 m long x 5 m high whose width was variable from 1 to 3 m. Experiments were performed with propane, both premixed as vapor and after a realistic spill of liquid within the channel. In some of the premixed combustion tests, baffles 1-2 m high were inserted into the bottom of the channel. Ignition of the propane-air mixtures revealed typical flame speeds of 4 m/s for the spill tests, and maximum flame speeds of 12.3 m/s in the premixed combustion tests. Pressure transducers recorded strong oscillations, but no quasi-static ovetpressure. 

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